Cost Analysis: PrintAll | CDC Econ Eval Tutorials

Introduction

Cost analysis is an economic evaluation technique that involves the systematic collection, categorization, and analysis of

program or intervention costs, and
cost of illness.

When Can We Use Cost Analysis?

Cost analysis can be used as a stand-alone evaluation method when

only one program is being assessed,
information about program effectiveness is not available, or
the interventions being assessed and compared are equally effective.

Cost analysis allows researchers to achieve cost minimization for the programs under consideration (with the goal to identify the least costly method to obtain a certain level of output).

Cost analysis can also be used together with effectiveness assessment techniques within the framework of three types of economic evaluation:

cost-effectiveness analysis,
cost-benefit analysis, or
cost-utility analysis.

Effectiveness assessment techniques vary, depending on whether cost-effectiveness analysis, cost-benefit analysis, or cost-utility analysis is used. Cost analysis techniques, however, are the same for all types of economic evaluations. The methods and skills presented in this self-study course can therefore be applied to cost-effectiveness analysis, cost-benefit analysis, or cost-utility analysis.

What are Costs?

Costs are the values of all the resources (e.g., labor, buildings, equipment, and supplies), tangible or intangible, used to produce a good or a service.

In everyday life we generally think of the financial or monetary cost of goods and services we consume. The "price tag" is what we refer to at the store. It is a convenient measure of cost: all the resources have readily available prices, and exchanges are based on monetary value.

Economists think of costs as consequences of choices. In the real world, resources are scarce. Because resources are limited, all necessary interventions cannot be implemented. When decisionmakers choose to implement a program, the resources expended will not be available for other possible uses.

For instance, the decision to allocate funds for a public health program renders these funds unavailable for education, housing, or defense spending.

Therefore, the true cost of a program is not just the amount of funds spent on it. It is also the value of benefits that would have been derived if the resources had been allocated to their next best use. Economists call it the opportunity cost of a resource or program.

Costs in Perfect Markets

Obtaining the opportunity cost of a resource is difficult. We have to identify the best alternative use of a resource and value the benefits foregone. In perfect markets, the market prices of resources reflect their opportunity costs. So we just have to collect market prices for goods traded in perfect markets to determine the opportunity costs.

Perfect market conditions exist when

numerous buyers and sellers can enter and withdraw from the market at no cost,
all buyers are identical,
all buyers possess the same relevant information, and
the goods and services traded are the same.

In reality, one or multiple conditions of perfect markets are violated in the majority of markets. Economists call them imperfect markets. Different methods are used to estimate the costs of resources when conditions for a perfect market are violated or the resources are not traded in the marketplace. Health-care markets do not meet the conditions for perfect markets for multiple reasons, among which are market power and asymmetric information.

Market power: The size and limited number of health insurance companies, the important participants in health-care markets who "buy" care from providers, gives them considerable market power to influence the prices of goods and services sold in that market. Health insurance companies representing multiple subscribers use their influence to negotiate discounts from hospitals and doctors (the "sellers"). Therefore, the prices paid to providers vary with the insurance status of patients and do not correspond to opportunity costs.

Asymmetric information: Consumers in health-care markets generally have limited information concerning the treatments that medical professionals offer them. Consumers are at a disadvantage to make fully informed choices. Economists refer to this difference in access to information between market participants as asymmetric information. Asymmetric information allows the sellers to charge prices for medical services that are higher than opportunity costs.

As a result, the charges for medical services rarely represent their true economic costs.

Methods of estimating true costs of medical services are considered below.

Costs in Imperfect Markets

The prices of tradable goods produced under perfect market conditions reflect their opportunity costs. We have to adjust the prices of goods purchased under imperfect market conditions to get correct estimates of their costs. The methods described below are different ways to derive true economic costs of resources in imperfect markets.

Using Cost-To-Charge Ratios (CCRs)

Market distortions (e.g., taxes and subsidies) are another reason for the discrepancies between the prices and economic costs.

The common method for estimating the true economic cost of medical services is to adjust the charges through the use of cost-to-charge ratios. Cost-to-charge ratios are coefficients developed by expert panels to convert charges for medical services to their true economic costs. Applying cost-to-charge ratios to medical service charges produces average estimates of true costs.

The Federal Register publishes Medicare cost-to-charge ratios every year, by state. The ratios are different for urban and rural areas.

Click this link to see the Cost-To-Charge Ratio Table

in Appendix A.

Micro-Costing

Micro-costing is a more precise method than is using cost-to-charge ratios but it is also more complex and time-consuming. Micro-costing involves identifying and determining a value for the resources actually consumed to produce the good or service.

For instance, instead of using a cost-to-charge ratio for a radiotherapy treatment session, we would have to estimate the cost of each component (e.g., medical consultant time, radiographer time, medical physics time, equipment, building and departmental overhead, and consumables).

Surveys

A survey can be used to estimate a person's willingness to pay (WTP) for a reduction in health risk or pain, or how much they would need to be paid to give up something.

The WTP approach is complex; a detailed discussion is presented in the Stated Preference Method

discussion in the Cost-Benefit Analysis tutorial.

Costs of Nontraded Goods and Services

Multiple health-care programs rely on nonmarket resources (e.g., volunteer time and donated goods and facilities), which do not require monetary compensation to secure their use. The estimated value of a nonmarket resource is called its shadow price. We discuss some common methods for estimating shadow prices below.

Using Market Prices for Similar Resources

Because nonmarket resources are not purchased in the marketplace, their costs are imputed based on the values of other resources.

Volunteer Time

Global substitute method: This method uses the wage rate of a paid worker that could be hired to do the job. It provides lower-end estimates.

Specialized substitute method: This approach uses the average wage of a specialist with appropriate skills for the task. This valuation technique takes into account the complexity of the task performed by volunteers, but problems might arise as it generates higher-end estimates.

Opportunity cost method: This approach uses the market wage that a volunteer is forgoing to perform the unpaid work. The opportunity cost method would yield a wider range of estimates depending on the skill and opportunity wage of the particular volunteer. This method allows volunteer work performed by a doctor to be imputed at a higher value than similar volunteer work performed by an unskilled worker.

Charity Goods

For other donated goods and services, we can use the market value of these inputs as the cost of the resources. For example, in the case of donated equipment or supplies, corresponding market prices can be found in catalogs or by contacting a supplier. The value of the physical space used by a program can be estimated from real estate listings for similar space in the area.

Using Similar Estimates from the Literature

One method for determining estimates might be to consult the published literature to assess how other researchers have handled the issue.

For example, a literature search might unearth previous studies in which values were assigned to volunteer time or to the pain and suffering associated with a medical condition.

Besides actual cost numbers, published studies often contain formulas which, if appropriate, can be replicated after some adjustments are made.

Discussing Qualitatively

Intangible costs are difficult to quantify, but they play an important role in patients' decisions. As a result, the majority of studies discuss the intangible costs qualitatively instead of attempting to estimate them by using sophisticated WTP methodology.

Note

Regardless of the nature of the resource or the method that is used to assess its value, be conscious of and consider all aspects of the true cost of a resource. For example:

Labor costs should include wages or salaries as well as benefits (e.g., paid vacations, health insurance, bonuses, and retirement fund contributions), and perquisites (e.g., the use of a car).
Supplies and equipment costs should include shipping charges, installation, and maintenance costs.
Transportation costs should include maintenance, gasoline, and insurance.
Whether or not sales taxes are included in the cost of a resource varies, depending on the study perspective. If the cost analysis is conducted from a societal perspective, taxes are considered a resource transfer and should not be included in the cost. If the cost analysis is conducted from any other perspective, sales taxes should be included, because they are part of the price paid to secure the use of that resource.

Why is Cost Analysis Important?

Cost analysis is an important component of all economic evaluation techniques. It is a useful tool for planning and self-assessment. Cost analysis is particularly useful for the following purposes:

Planning and Cost Projections

Cost analysis can be used as a tool for

developing and justifying budgets, and
determining the level of funding changes necessary to achieve a desired change in disease prevalence/incidence.

Assessing Efficiency

A program is considered efficient when the maximum amount of output (i.e., cases treated or persons screened) is produced from the given level of inputs (i.e., resources).

Cost analysis makes it possible to assess the efficiency of programs by

comparing cost profiles from equally effective programs, and
identifying cost categories for further efficiency studies.

For instance, tuberculosis-control programs can be compared by evaluating the disparity between unit cost per output: cost per tuberculosis case treated or cost per person screened.

If a variation in cost per unit output is observed, we might decide to study further to determine the possible reasons.

If we do not find a justification for higher costs per unit (e.g., a higher rate of MDR-tuberculosis rate in the target population) we might need to reassess the program structure and methods to improve efficiency.

Assessing Priorities

Cost analysis provides information on health resource allocation. We can use this information to

examine how resource use reflects national, state, and local health priorities, and
examine how expenditure profiles of similar programs vary from one another. Cost patterns from a cost analysis might indicate that previous priorities need to be reassessed by giving consideration to emerging trends.

Accountability

Cost analysis involves tracking expenses, which allows us to know how the funds are spent and whether they are spent as intended.

Assessing Equity

Cost analysis can help us to assess how health resources are distributed among various population groups.

For instance, cost analysis can indicate whether a program spends more resources per capita in urban areas than in rural areas and whether the difference is the result of allocation mechanisms or of differences in need.

Framing a Cost Analysis

When you are conducting a cost analysis, the first step is to determine a detailed research strategy or framework that will later guide the data collection and analysis efforts. This stage is referred to as study framing.

We discussed study framing in detail for all types of economic evaluation in the Framing

tutorial. Next, we will see how the concepts and steps in that tutorial are applied for framing a cost analysis.

We follow seven steps to frame a cost analysis.

1. Defining the Problem

Conducting a study involves considerable expenditure of resources; therefore, research dollars must be allocated efficiently. In the first step of framing a cost analysis, we need to identify the problem and the reasons that justify expending the limited resources on the study. We have to consider the following questions:

What is the problem to be analyzed?
Why is it important?
What aspects of the problem need to be explained?
What questions need to be answered?

Example: Antigua's Health Education and Condom Distribution (HECD) Program

This cost analysis was conducted in 1992 in the Caribbean's leeward island.

What was the problem to be analyzed?
- To determine the cost of the HECD program.
Why was it important?
- Funding for an AIDS prevention program among persons at high-risk was coming to an end. Without adequate funding, the program would be shut down. As a result, human immunodeficiency virus (HIV) infection rates could increase.
What aspects of the problem needed to be explained?
- Cost data were needed to evaluate the program and identify resources to continue its operation.
What questions needed to be answered?
- What was the annual cost of running the HECD program?
- What resources are needed to continue the program?

2. Defining the Options

To obtain estimates that are as accurate as possible, all relevant organizational and technological aspects of available options/interventions must be considered, which includes defining the items below.

Interventions	The nature of the intervention(s).
Comparisons	What will this program be compared with? Current practice can always be used as a baseline for comparison. (Can we do better than what we are currently doing?).
Target population	What are the populations that the intervention is designed to reach?
Delivery site	Where will the intervention take place?
Personnel	Who will deliver the services? Several categories of personnel (e.g., physicians and public health nurses [PHNs]) could be involved.
Technology	Laboratory tests and surgical operations, for example.
Timing	The beginning of the school year or of the calendar year, for example.

Example: Antigua's Program Options

Interventions	Health education and condom distribution.
Comparisons	Implications of program termination.
Target population	Commercial sex workers from the Dominican Republic.
Delivery site	19 locations (bars, brothels, boarding houses, and truck stops).
Personnel	Two outreach workers.
Technology	Condoms and printed materials.
Timing	On an ongoing basis during January 1990–September 1991.

3. Defining the Audience

The structure of the analysis depends on who will be using the results of the cost analysis. We have to consider the following questions:

Who will be using the results of the analysis?
What are the information needs of the audience?
How will the results be used?

Example: Antigua's Program Audience

Who was the audience for the cost analysis?	Ministry of Health of Antigua Caribbean Epidemiological Center (CAREC) Family Health International/AIDSTECH
What were the information needs of the audience?	How much does the program cost? Is it sustainable?
How would the audience use the results?	To compare with other projects To measure the involvement of the different funding agencies

4. Defining the Perspective

The study perspective determines which costs are relevant and should be included in the cost analysis. The perspective takes into account who bears the costs and who gains from available interventions. A cost analysis can be conducted from any or all of the perspectives indicated below, from the narrowest to the broadest.

Patient/Family:	Costs incurred by patient/family are considered.
Provider:	Costs related to providing the health services are considered (e.g., clinics and hospitals).
Payer:	Costs incurred by persons or entities responsible for financial costs of health services are considered (e.g., insurance companies, employees, and employers).
Health system:	The costs related to providing health care, including all categories of providers, are considered.
Society:	All costs, regardless of who incurs them, are considered.

Example: Antigua's Program Perspective

The cost analysis was conducted from the payer/funding entity perspective.

The choice of a perspective was driven by the audience for the analysis.

5. Defining the Time Frame

The time frame must be long enough to capture the full extent of the program costs (the costs of the intervention itself) and of the side effects. The time frame must be long enough to account for

program start-up and maintenance costs,
seasonal variations, and
cost of intervention, including side effects.

Example: Antigua's Program Time Frame

The time frame for the cost analysis was 1 year.

Reason: All agencies involved in the program allocate funds on a yearly basis.

6. Defining the Analytic Horizon

Following are examples of conditions when the length of the analytic horizon is not apparent and careful consideration is required to determine it.

The costs and benefits derived from an intervention occur at different times, as is the case with prevention strategies (costs now, benefits later).

A horizon that is too short will underestimate the value of the intervention, and the impact could be life-long.
Interventions with different timelines are to be compared.

We have to choose an analytic horizon that is:

long enough to capture the full costs and effects of programs with an impact that occurs at different times, and
short enough that future costs and benefits are not uncertain.

The time frame and analytic horizon diagram below illustrates a time frame with a much longer analytic horizon.

Time frame and analytic horizon

7. Choosing a Format

Depending on the availability of data and resources, we can choose to use one of three formats:

Retrospective analyses: Can be conducted when the intervention of interest is already in place or has been carried out previously. When the analysis starts, the costs have already been incurred.
Prospective analyses: Costs have not yet been incurred when the study starts. We will therefore track the costs as they occur.
Models: Costs are based on estimated values from other studies.

Example: Antigua's Program — Retrospective

The cost analysis followed a retrospective format:

Example: Antigua's Program — Prospective

A possible prospective format:

Example Summary: Antigua's HECD Program

Antigua's Health Education and Condom Distribution (HECD) Program
The research design was as follows:
Intervention
Nature	Health education and condom distribution
Target population	Commercial sex workers from the Dominican Republic
Delivery site	19 sites: STD clinic, brothels, truck stops, bars, and boarding houses
Personnel	2 outreach workers, 1 supervisor, and 1 administrative assistant
Technology	Condoms and printed materials
Timing	Ongoing
Audience	Program payers
Perspective	Program payers
Scope	The analysis included program costs for both program components: health education and condom distribution
Study time frame	1 year
Study format	Retrospective
Outcome measures	Costs, Number of condoms distributed, and Number of persons reached with health education talks
Summary measures	Cost per condom distributed and Cost per person reached with health education talks

Cost of the Intervention or Program

The cost of intervention is a measure of the value of all resources used in the intervention. The cost of intervention is an important part of the decision to use one intervention over another. Knowing about the costs provides clues as to whether there is too much spending on less desirable programs or too little spending on highly desirable programs.

The cost of intervention can be used:

by both internal and external reviewers as a tool to monitor the level of performance of programs, and
for manifold purposes, as described in the previous chapter.

An estimation of the cost of intervention is conducted by framing the cost analysis, developing a cost inventory, evaluating resource use, and calculating cost analysis results.

Framing the Cost Analysis

The steps involved in framing cost analysis have been covered in an earlier section. Please see Framing a Cost Analysis

for a detailed discussion.

Developing a Cost Inventory

The next step involves developing an inventory of the resources required for the intervention. The cost inventory comprises a comprehensive list of resources with unit and total cost of each resource. Costs are generally classified as direct, indirect, and intangible costs.

Direct costs are defined as the values of all resources expended on design and implementation of the health intervention (e.g., personnel, lab tests, and facilities [rent and utilities]). By definition, direct costs can be either medical or nonmedical. The costs related directly to providing a treatment are categorized direct medical costs.

For instance, the costs of vaccines, syringes, and nurses' salaries will be included in direct medical costs of a vaccination program. Patients' expenses for transportation to vaccination clinics will be included as part of direct nonmedical costs.

Indirect costs or productivity losses are the income forgone because of changes in productivity as a result of health intervention or illness (e.g., time lost from work or decreased productivity because of health problems).

Intangible costs are the nonmaterial costs (e.g., emotional anxiety, fear, pain, and stigmatization). Intangible costs impose a major burden on a patient. Quantifying intangible costs is difficult, and these costs are not included in the majority of studies. However, we must not forget to account for intangible costs, because they might be a major factor that affects patients' decisions.

Example: Cost Inventory

Classification Systems

Major Classification Systems

Below are examples of the list of resources in cost inventory, which is usually categorized and presented in a classification system.

Line item or functional system: costs are classified according to use or function of resources. For example:
- Personnel costs
- Facilities and equipment costs
- Drug costs
- Transportation costs and travel expenses
Level of responsibility
- Federal
- State
- Local
Sources of funding
- Federal
- State
- Local
or
- Private for profit
- Private not-for-profit
- Public
Activity areas:
- Training costs
- Curriculum development costs
- Marketing costs

Classification by Cost Type

Depending on the perspective of our analysis, we can also classify and present all the costs as components of program costs, costs to participants, and costs to others.

Program Costs

Program costs list the value of all the resources expended on implementation and maintenance of the intervention. The diagram below illustrates the types of costs/resources that need to be considered in the majority of health-care programs.

Costs to Participants

Costs incurred by participants are either

out-of-pocket expenses (expenses incurred by participants that are not accounted for in the program costs), or
productivity losses.

Costs to Others

A health intervention can cause adverse events in persons who are not directly participating in the program. If our study has a societal perspective, we must include the resulting costs incurred by others. The chart below illustrates how a typical list will look.
Costs to others.

Combining Classification Systems

It is possible to use two classification systems simultaneously. For instance, costs can first be classified by source of funding and then by line item. The use of multiple classification schemes is helpful when an intervention or program is complex or multitiered. Below is an example.

Cost Inventory Summary

To develop a cost inventory, we prepare a comprehensive list of all resources and present them in a classification system that is most suitable for our study. We make sure that we include resources obtained without monetary exchange:

volunteer time
caregivers' time
patient's time
in-kind contributions/donated materials, and
resources previously purchased.

We also make sure to include

resources that are hard to measure or value, and
resources used in small amounts.

Evaluating Resource Use

Having developed the cost inventory, we can measure the quantity of the resources used in the delivery of the intervention and assign values to them. We characterize costs as either fixed or variable, depending on their variation with changes in program activity level.

Fixed Program Costs

The fixed costs of a program or intervention are those that, in short run, do not vary with the level of activity. Costs associated with the facility (e.g., rent and utilities) and personnel costs for support staff (e.g., receptionists and information services staff) are the most common fixed costs. These costs are often incurred at the beginning of program implementation and are frequently referred to as start-up costs.

We can account for facilities cost by adding the cost of space, maintenance costs, and the costs of utilities. Costs for facilities are usually recorded as either the cost per unit (e.g., cost per square foot) or the total cost for the facility. The equations below can be used to determine the facility's costs for programs sharing space in an existing facility.

Facilities costs

Additional facility space used by the program

Cost per square foot for space and utilities

Facilities costs

Total facility cost for space and utilities

(

Facility time used by program

Facility time used by all programs

)

We can calculate the costs for administrative and staff support as a proportion of the staff time spent on this particular intervention. The equation below is used to determine the cost of administrative and staff support associated with a program.

Administrative costs

Proportion of administrator's time spent on intervention

Administrator (salary + benefits)

Support costs

Proportion of support staff time spent on intervention

Support (salary + benefits)

Administrative and staff support costs

Administrative costs

Support costs

Variable Program Costs

The variable costs of a program are those that change as the level of activity changes. Examples of variable costs include provider time, medications, tests, material, and supply costs. The typical approach to measuring variable costs is to identify the quantity of the relevant resource and multiplying it with per unit price.

Provider cost is determined for each provider type and service by using the equation below.

Provider cost

Provider (salary + benefits)

Average duration of service

Number of services provided in period

Material and supply costs can be determined by the equation below.

Material and supply costs

Specific resource

Cost per unit

Number of units used in period

Sources

We can use information from various sources to assess the resources used. And we might eventually use more than one method. The main sources of information are listed below.

Primary data collection
- Questionnaire surveys (require large numbers of survey participants to calculate unit costs)
- Observational surveys (require large numbers of observations to calculate unit costs)
- Medical records
- Accounting and payroll systems
Published literature
Professional guidelines/practice

Calculating Cost Analysis Results

The first series of calculations computed on the basis of the cost information previously collected is referred to as the base-case scenario. It is based on the assumptions about resource use and value that the researcher believes most closely reflect the policy/program/intervention's true level of resource use (best estimate). These calculations include

total costs,
average costs, and
marginal costs.

Total Cost

The total cost (TC) of a program or an intervention is derived by adding all the costs incurred in producing a given level of output. So it includes the cost of all the personnel, the supplies, and the equipment that were identified in the cost inventory.

This measure of cost is simple to calculate. Mathematically, total costs are expressed as

(Q₁ x P₁)

(Q₂ x P₂)

+...+

(Q_n x P_n)

where

Q₁	=	Quantity of Resource 1	P₁	=	Value of Resource 1
Q₂	=	Quantity of Resource 2	P₂	=	Value of Resource 2
Q_n	=	Quantity of Resource n	P_n	=	Value of Resource n

Total costs can be used to

rank diseases by economic burden
measure the cost of treating a disease, and
measure the cost of a program relative to its budget.

Although it is a useful and simple measure of costs, TC has the following limitations:

As an aggregate measure, TC is difficult to interpret
It difficult to use TC to compare programs or interventions whose outcomes differ.

Average Cost

The average cost (AC) is the cost per unit of output (e.g., cost per patient treated or cost per child immunized). AC is computed by dividing the total cost by the number of participants or other relevant intervention units. The formula is

where

AC	=	Average cost
TC	=	Total cost
Q	=	Units of output

Example: Calculating Average Cost for the Antigua HECD Program

Total field costs for the Antigua HECD Program were $2,259 per month. On average, 4,805 condoms were distributed each month.

In this situation, the average cost per condom distributed was

$2,259

4,805

$0.47 per condom distributed

When Can Average Cost Be Used?

The average cost can be used:

To Compare Subgroups

In the Antigua example, the cost analysis reported an average cost per condom distributed for two different settings: one for an STD clinic, and one for the outreach program. The cost at the STD clinic was higher, because when people come to the clinic, they receive additional services (beside condoms).
To Compare Efficiencies of Various Programs and Interventions

Higher average cost might indicate that the resource utilization is less efficient and further study is warranted to find out the reason. It might turn out that the reason for higher average cost is less favorable conditions for treatment (e.g., harmful agents with higher resistance to drug treatment or difficulty in reaching the target population).

To Determine Economies of Scale

Economies of scale occur when the average cost per unit produced decreases as the level of activity increases because, in the short term, fixed costs can be spread over a larger number of units. Potential economies of scale can be identified by calculating and comparing the average cost for several output levels.

An Example: Clinic Costs

For a clinic, let us assume that for each output level included in the table below, a program incurs the corresponding variable and fixed costs. Total and average costs are also given in the table.

Symbol	Quantity	Data
A	Number of patients	10	20	30	40	50	60	70
B	Variable cost	10	10	10	10	10	10	10
C	Fixed cost	150	150	150	150	150	400	400
D	Total cost [(A x B) + C]	250	350	450	550	650	1000	1100
E	Average cost [D / A]	25	17.5	15	13.75	13	16.6	15.71

If the program treats between 10–50 patients per day, a potential for economies of scale exists: adding more patients would lead to a decrease in the average cost per patient. For example, increasing output level from 40 to 50 patients per day would decrease the average cost from $13.75 to $13 per patient.

After the program treats 50 patients per day, the average cost per patient rises again. In this example, diseconomies of scale set in.

Marginal Cost

The marginal cost (MC) is the resource cost associated with producing one additional or one less unit within the same intervention/program. Because MC is an indication of the amount of additional resources that must be expended to serve additional patients, it is useful in making program expansion decisions. Usually, MC is calculated from data on the basis of the cost of a larger increase in outputs.

The formula for calculating MC is

Change in total costs

Change in quantity produced

(TC' – TC)

(Q' – Q)

where

Q	=	Lower level of output
Q'	=	Higher level of output
TC	=	Total costs at lower output level
TC'	=	Total costs at higher output level

Example: Marginal Cost

Problem

A public health nurse can screen 25 patients per day. Her salary is $160 per day. Screening and lab costs are $25 per patient. If >25 patients are scheduled, the nurse must call and ask that a nurse's aide help her. The nurse's aide salary is $100 per day.

Questions

What is the MC of screening one additional patient

if 24 patients are already scheduled?
if 25 patients are already scheduled?

Answers

Situation A: 24 Patients Scheduled

By using the formula, the marginal cost of adding one patient is

(TC' – TC)

(Q' – Q)

where

TC'	=	Total costs, higher output level	=	($160 + ($25 x 25)) = ($160 + $625) = $785
TC	=	Total costs, lower output level	=	($160 + ($25 x 24)) = ($160 + $600) = $760
Q'	=	Higher output level = 25
Q	=	Lower output level = 24

therefore

(($785 – $760) / (25 – 24))

($25 / 1)

$25 per additional patient

In this situation, the program can admit one additional patient without exceeding its operating capacity. No additional fixed costs are required, because help from the nurse's aide is not needed. The marginal cost will therefore comprise only the variable costs associated with treating the additional patient (i.e., the screening and lab costs [$25]).

Situation B: 25 Patients Scheduled

By using the formula, the marginal cost of adding one patient is

(TC' – TC)

(Q' – Q)

where

TC'	=	Total costs, higher output level	=	(($160 + 100) + ($25 x 26)) = ($260 + $650) = $910
TC	=	Total costs, lower output level	=	($160 + ($25 x 25)) = ($160 + $625) = $785
Q'	=	Higher output level = 26
Q	=	Lower output level = 25

therefore

(($910 – $785) / (26 – 25))

($125 / 1)

$125 per additional patient

For the 26th patient, the variable cost associated with the additional patient is $125. It includes not only the original variable cost of $25, but also the salary of the nurse's aide, $100.

For the 27th and higher patients, the variable cost reverts to $25 per patient.

Conclusion

This example reveals that the cost of marginally increasing a program's level of output varies, depending on whether or not the program is operating at full capacity. In Situation A, a patient can be added for a cost of $25 dollars (or the sum of variable costs), whereas in Situation B, the marginal cost increases to $125 (or the sum of variable costs plus additional fixed costs).

When Can Marginal Costs Be Used?

The marginal cost measures the effect of making an additional investment in the intervention, and can be used to

evaluate the change in total costs that will result from a change in program activity level,
evaluate the change in total costs that is needed to produce change in outcomes, or
determine the optimal activity level of a program or intervention.

As a rule, programs should target their activity level so that average and marginal costs are equal.

As long as the marginal cost is lower than the average cost, economies of scale are possible, and increasing output decreases average cost.

When average cost equals marginal cost, no additional economies of scale can be achieved (i.e., expanding output increases average cost). At that level, the program

operates at its maximum technical efficiency (i.e., it is taking maximum advantage of the resources being used in its implementation), and
represents the least costly method (in terms of total costs) to produce that level of output.

Calculating MC and average cost for a series of capacities enables the decisionmaker to

identify any potential for economies of scale, and
take maximum advantage of the resources invested while minimizing total costs.

Sensitivity Analysis

The information obtained in developing the cost inventory and calculations of various cost measures provides what we call our base-case scenario. Cost analysis, like other types of economic evaluation, almost always involves uncertainty about certain or all of the parameter estimates that are used in the study. Typical sources of uncertainty include

measurement errors,
conflicting or biased estimations from the literature,
omission of important cost components, and
an inappropriate time frame/analytical horizon.

We take the uncertainty into account by conducting a sensitivity analysis (SA) and examining how "sensitive" the analysis results are to a change in base-case parameters. A sensitivity analysis should always be conducted.

An Example: The Role and Importance of Sensitivity Analysis

A state tuberculosis-control program has decided to implement a targeted screening program to identify children infected with tuberculosis at a local public school where 52% of students are newly arrived immigrants. The program will be implemented once a year during a 10-day period. All 400 children in the school will be tested. Children who test positive will be administered treatment for latent tuberculosis infection to decrease the likelihood that the condition will evolve into active tuberculosis disease. A cost analysis is conducted to estimate the resources needed to implement this targeted screening program.

Program planners have been unable to obtain detailed information from school officials regarding the children's countries of origin. Therefore, estimating the prevalence of latent tuberculosis infection among the children might be difficult. This challenge causes difficulty in assessing how many children will require treatment and how much the program will ultimately cost.

In their base-case scenario, program planners assume a 15% infection rate among foreignborn children, which reflects the "background" infection rate in the local community as measured by the local public health department. Because we know the number of children in the school and the proportion that are foreignborn, we can calculate the number of infected children the program can expect to identify and treat, based on the base-case assumptions:

400

0.52

0.15

The cost analysis results for the base-case scenario are as follows:

Cost	Amount
RN (2)	$4,000
LPN (1)	$1,000
Skin test/medical supplies ($20 * 400)	$8,000
LTBI treatment ($500 * 31)	$15,500
Total intervention costs	$28,500

Because program planners are uncertain about the prevalence of tuberculosis infection in the school, they decide to conduct a sensitivity analysis around the rate of latent tuberculosis infection. They decide to vary the rate by 5-point increments between 0 and 30%. Here are the results of their sensitivity analysis:

Prevalence among foreignborn students	Expected number of infected students	LTBI treatment costs	Total costs
0%	0	0	$13,000
5%	400 x 0.52 x 0.05 = 11	11 x 500 = $5,500	$18,500
10%	400 x 0.52 x 0.10 = 21	21 x 500 = $10,500	$23,500
15%	400 x 0.52 x 0.15 = 31	31 x 500 = $15,500	$28,500
20%	400 x 0.52 x 0.20 = 42	42 x 500 = $21,000	$34,000
25%	400 x 0.52 x 0.25 = 52	52 x 500 = $26,000	$39,000
30%	400 x 0.52 x 0.30 = 63	63 x 500 = $31,500	$44,500

These results indicate that total costs of the intervention vary substantially with the estimated prevalence. Program planners might need to invest more effort into estimating the actual prevalence of latent tuberculosis infection among foreignborn students at the school to plan and budget for the intervention more effectively.

Notes:

The sensitivity analysis around latent tuberculosis infection prevalence could have been conducted using only one or two alternative values (best-case and worst-case scenarios, for example).
Prevalence of latent tuberculosis infection among foreignborn children is not the only parameter that could be varied in a sensitivity analysis in this situation.

For example, program planners appear to assume that only foreignborn children are at risk for latent tuberculosis infection. A sensitivity analysis around the rate of infection among U.S.-born students could also be conducted to challenge this assumption.

Types of Sensitivity Analysis

The three types of sensitivity analysis below are commonly conducted, depending on the objective and the number of parameters that are changed to derive the results.

One-way SA:	One parameter is changed at a time and the results are recalculated.
Multiway SA:	Two or more parameters are changed simultaneously.
Threshold analysis:	For each parameter or for a set of parameters, we determine the critical values beyond which the conclusions of the analysis change.

The strengths and weaknesses of one-way and multiway sensitivity analyses are summarized in the table below.

	One-way	Multiway
Pros	straightforward, intuitive, easy to do	takes into account the possibility that parameters are interdependent
Cons	assumes parameters are independent	more complex

Threshold Analysis

Threshold analyses should be conducted only around continuous variables (i.e., variables that can take on any fractional or integer value). Height, weight, prevalence, and incidence are examples of continuous variables that are infinitely divisible and that can take on an infinite number of values between two integers.

Variables that represent counts (e.g., 1, 2, 3, and 4) are discrete variables. (Examples of discrete variables are the number of patients or the number of test kits used.) Threshold analyses should not be conducted around discrete variables.

A threshold analysis can be conducted as a one-way or as a multiway analysis. In the multiway analysis, two or more values are varied simultaneously.

For example, a threshold analysis conducted around the prevalence rate of a genetic disorder can help determine the point at which implementing a universal screening program becomes less costly than a targeted screening strategy. The figure below illustrates the results of the corresponding threshold analysis.

For each strategy in this example, the average testing cost per patient was calculated for all disease prevalence rates between 5% and 30%. The results were used to create this graph.

The intersection between the two curves indicates the disease prevalence at which the average testing cost is the same for both strategies. When disease prevalence is 22.5%, the average cost of testing a patient through targeted screening or through universal screening is approximately $23.50.

When prevalence is less than 22.5%, the targeted screening strategy is less costly.

When prevalence is higher than 22.5%, universal screening is less costly (in terms of average cost per patient screened).

Case Study: Hepatitis B Vaccination Program — Denver, CO, 1996–1997

Context

In 1996, the Colorado State Board of Health mandated that all students complete a 3-dose hepatitis B vaccination series before entering the 7th grade. Consequently, the Denver Public School (DPS) System offered a free, voluntary, school-based, hepatitis B vaccination program to students in the 6th grade during the 1996–97 school year.

This case study estimates and compares the program costs of the vaccine delivery programs for the school-based system and for the network HMOs.

Source of This Study

Deuson, RR, Hoekstra, EJ, et al. Denver School-Based Adolescent Hepatitis B Vaccination Program: a cost analysis with risk simulation. American Public Health 1999: 89:1722–27

Methods

Study population:	A total of 4,665 6th-grade students enrolled in 18 Denver Public School (DPS) middle schools at the beginning of the 1996–97 school year.
Study design:	Retrospective direct and indirect cost analysis to estimate cost per dose for A school-based program, and PacifiCare, a network HMO.
Study perspective:	Societal.

Calculating Societal Costs

All costs were classified into startup costs and ongoing costs.

School-Based Program

The three cost components of the school-based program are estimated as follows:

Educational and Outreach Costs

Educational presentations regarding the hepatitis B vaccine were made to the parents, guardians, and students. Information packets with a consent form for the vaccine series were mailed to parents or guardians. If the consent form was not returned, an additional follow-up packet was mailed.

Program costs included the items below.

Personnel time devoted to the development of educational material and training.

Costs of personnel time are calculated by multiplying the salaries and benefits of relevant personnel by the amount of personnel time devoted to the particular project (i.e., development, training, and administration).
Educational materials.
Costs of supplies, including consent forms.
Postage, copying, and their miscellaneous supplies.
Calling costs.

Vaccination Costs

The vaccination costs at each of the school clinics were tallied. These costs comprise

Personnel time, which consists of
- Staff time: The estimated cost of staff salaries and benefits multiplied by the time devoted to the project.
- Volunteer time: The cost of volunteer time is imputed on the basis of the cost of hiring a paid worker with appropriate skills to do the job.
Cost of supplies.
Cost of vaccine.

Management Costs

Program management costs included all labor costs associated with the design of school-based clinics' vaccination, hiring, and supervision of staff.

PacifiCare HMO Vaccination Delivery Program

The societal cost for the PacifiCare program includes the cost to the PacifiCare network HMO, cost to the patient.

Cost to the PacifiCare Network HMO

The cost to HMO includes the items below.

Vaccine costs: PacifiCare reimburses network physicians for the average wholesale price of the vaccine, $68.06 per dose, plus a 10% markup.
Administration costs: A total of $7.50, which covers
- administering the injection,
- supplies other than the vaccine (alcohol, swab, cotton, syringe and needle, and bandage), and
- documentation.

Cost to the Patient

The cost to the patient includes

Patients' out-of-pocket expense: copayment ($10).
Cost of work lost by the parents: The cost of work loss is calculated as the work income forgone by a parent when taking his or her child to have the vaccine administered.
The estimated time for administration of the vaccination series is 9 hours (three clinic visits of 3 hours each). For working parents, this time had to be taken either as sick leave, vacation time, or leave without pay, each therefore carrying an opportunity cost.

Because no information was available regarding the parents' employment status or income, estimates of work loss costs are determined based on 1996 US Bureau of the Census data for incomes of married-couple families with children aged 6–17 years.
Estimates were calculated for all combinations of employment status for husband and wife (full-time work, work, or no-work). Researchers assumed that on average, women earned 74% as much as men in 1996.

Total Costs

Costs of providing 8,886 doses of hepatitis B vaccine to 3,359 6th-grade students in school-based vaccination clinics — Denver, CO, September 1996–May 1997

	Education/ Outreach	Vaccine delivery	Program management	Total
Start-up costs
Development	4,196
Supplies	245	340
Personnel			20,497
Total start-up costs	4,441		20,497	25,278
Ongoing costs
Training	27,266
Supplies	17,520	2,441
Vaccine		77,308
Personnel		46,808	75,252
Gift certificates			425
Total ongoing costs	44,786	126,557	75,677	247,020
Total costs	49,227	126,897	96,174	272,298

Unit (Per Dose and Per Series) Costs

Cost-Effectiveness Ratios of the School-Based Hepatitis B Vaccination Program — Denver, CO, September 1996–May 1997

	Mean (SD)	95% Confidence interval
Including all costs
Per dose	30.64 (0.94)	(28.80, 32.48)
Per completed series	95.29 (2.94)	(89.53, 101.05)
Excluding start-up costs
Per dose	27.79 (0.93)	(25.97, 29.61)
Per completed series	86.45 (2.90)	(80.77, 92.13)

Parents' Productivity Loss Per Visit

Parents' work status	$ Cost Mean (SD)
Both worked full-time	42.31 (2.63)
Wife worked full-time, husband worked	41.14 (2.59)
Wife worked full-time, husband did not work	46.69 (4.07)
Wife worked, husband worked full-time	40.36 (2.53)
Both worked	39.10 (2.44)
Wife worked, husband did not work	34.52 (3.48)
Wife did not work, husband worked full-time	10.17 (1.58)
Wife did not work, husband worked	9.25 (1.43)
Neither worked	9.06 (0.94)

Test Your Understanding

Please enter your answer to each question before you click on "Our Answer".

The director of a childhood vaccination program wants to evaluate the cost of one of the program's interventions targeting hard-to-reach populations. He asks the program accountant for a list of direct costs. The accountant provides a list of expenses related to the intervention for the previous 6 months and comments

"Because you asked for direct costs only, I did not include overhead expenses."

Should the director be satisfied with the list of costs provided by the accountant? Why or why not?

Our Answer

The program director should not be satisfied with the list of costs provided by the accountant. Contrary to accounting practices, economic evaluation considers overhead expenses to be a direct cost.
The list of direct costs associated with the implementation of the intervention should have included a share of overhead costs.
What could be some of the direct costs associated with implementing an early-detection program for breast cancer that includes free mammograms, counseling sessions, and the distribution of educational material?
Our Answer
Potential direct costs include

labor costs (e.g., X-ray technician, physician, and counselor),

space costs (e.g., X-ray room, counseling rooms, waiting room, and office space),

equipment costs (e.g., X-ray machine and computer for record keeping),

medical supply costs (e.g., X-ray film and reagent), and

educational supply costs (e.g., brochures and posters).
What could be some of the indirect costs associated with implementing an on-the-job weight management program at a manufacturing plant?

Our Answer

The time off from work taken by employees to attend program sessions is an indirect cost. It represents a productivity loss from the company's perspective.
Leisure time spent after work to attend sessions is also an indirect cost, incurred by program participants.

Nurse Betty is responsible for tuberculosis-control activities at the county health department. Her clinic is located in a building leased by the county from the city. For transportation, Nurse Betty uses her personal vehicle and is reimbursed for mileage.

The clinic is equipped with a portable isolation unit for infectious patients. Patients who need chest x-rays are referred to the local hospital.

Nurse Betty spends the majority of her time in the field, administering tuberculin skin tests to patients suspected of being infected with tuberculosis, collecting sputum samples for smears and cultures with her portable nebulizer, and administering drug treatment.

Nurse Betty uses a laptop and a database software program to keep track of her patients.

From this brief description, identify fixed and variable costs associated with this tuberculosis-control program.

Fixed costs	Variable costs

Our Answer

Fixed costs	Variable costs
Nurse Betty's salary	Transportation: mileage
Clinic space	Chest x-rays
Portable isolation unit	Tuberculin skin test kits
Portable nebulizer	Sputum collection kits
Laptop/software	Laboratory costs
	Drugs

Note:

The cost of a resource can have both a fixed and a variable component. For instance, the purchase of a portable isolation unit or a nebulizer is a fixed cost. However, the maintenance costs associated with this equipment are variable costs, if they are related to how intensively the equipment is used.

The following cost inventory has been compiled (assume that necessary adjustments for inflation and capital costs annuitization have been made):

Resource	1996	1997	1998	1999	2000
Personnel	$300,000	$400,000	$300,000	$350,000	$400,000
Supplies	$5,000	$5,000	$6,000	$7,000	$5,000
Equipment	$5,000	$5,000	$5,000	$5,000	$5,000
Travel	$3,000	$2,000	$5,000	$4,000	$6,000
Equipment	$2,000	$7,000	$3,000	$2,000	$4,000

Calculate the total program costs for 1999.

Our Answer

Total costs for 1999 are

Costs1999

Personnel costs

Supplies costs

Equipment costs

Travel costs

Training costs

substituting

Costs1999	=	$350,000	+	$7,000	+	$5,000	+	$4,000	+	$2,000
	=	$368,000

From the data in question 5, calculate the total program costs over the 5-year time frame.

Our Answer

Total costs during the 5-year time frame are

Total costs

Costs1996

Costs1997

Costs1998

Costs1999

Costs2000

where

Costs1996	=	$300,000	+	$5,000	+	$5,000	+	$3,000	+	$2,000
	=	$315,000
Costs1997	=	$400,000	+	$5,000	+	$5,000	+	$2,000	+	$7,000
	=	$419,000
Costs1998	=	$300,000	+	$6,000	+	$5,000	+	$5,000	+	$3,000
	=	$319,000
Costs1999	=	$350,000	+	$7,000	+	$5,000	+	$4,000	+	$2,000
	=	$368,000
Costs2000	=	$400,000	+	$5,000	+	$5,000	+	$6,000	+	$4,000
	=	$420,000

so that

Total costs	=	$315,000	+	$417,000	+	$319,000	+	$368,000	+	$420,000
	=	$1,841,000

From the data in question 5, calculate the average annual cost over the same 5-year time frame.

Our Answer

Average annual costs during the same 5-year period are

$1,841,000 / 5 = $368,000 per year

Let us assume that a cost analysis has determined that the fixed cost associated with a particular intervention is $50,000 per year. Variable costs are $120 per patient.

Calculate the average cost per patient for each of the numbers of patients seen in the table below.

Number of patients treated	Average cost per patient
1
5
10
20
50
100

Our Answer

Number of patients treated	Average cost per patient
1	(50,000 + 120) / 1 = $50,120
5	[50,000 + (120 x 5)] / 5 = $10,120
10	[50,000 + (120 x 10)] / 10 = $5,120
20	[50,000 + (120 x 20)] / 20 = $2,620
50	[50,000 + (120 x 50)] / 20 = $1,120
100	[50,000 + (120 x 100)] / 20 = $620

On the basis of the information provided in the table below, identify the range of output levels over which economies of scale are possible.

Output level (Number of units)	Total costs	Average cost per unit of output
1	$100,000
2	$120,000
3	$140,000
4	$150,000
5	$200,000
6	$250,000
7	$300,000

Our Answer

Output level (Number of units)	Total costs	Average cost per unit of output
1	$100,000	$100,000
2	$120,000	$60,000
3	$140,000	$46,667
4	$150,000	$37,500
5	$200,000	$40,000
6	$250,000	$41,667
7	$300,000	$42,857

Economies of scale are possible when the output level is 1–4. Over that range, the average cost decreases as output increases.

When the output level reaches 4 units, the average cost per unit produced starts increasing. Diseconomies of scale set in.

Assuming that fixed costs are constant at all output levels, calculate the marginal cost on the basis of information provided regarding output level and total costs.

Output level	Total costs	Marginal cost
0	$500
1	$510
2	$520
3	$530
4	$550
5	$560
6	$565

Our Answer

Output level	Total costs	Marginal cost
0	$500	$510 – $500 / (1 – 0) = 10 / 1 = $10
1	$510	$520 – $510 / (2 – 1) = $10 / 1 = $10
2	$520	$530 – $520 / (3 – 2) = $10 / 1 = $10
3	$530	$550 – $530 / (4 – 3) = $20 / 1 = $10
4	$550	$560 – $550 / (5 – 4) = $10 / 1 = $10
5	$560	$565 – $560 / (6 – 5) = $5 / 1 = $5
6	$565

The coordinator of the after-school program at the local middle school is organizing a field trip for her students.
Regulations require that one adult be present for every 10 students. The group will rent a bus, which holds 33 passengers (not including the driver), for $150. If more than 33 passengers go on the trip, an additional (smaller) bus will need to be rented for $90. The purpose of the trip is to visit a famous regional museum. The admission price to the museum is $8 per person.
A total of 30 students have signed up by the registration deadline. What is the total cost of the trip? How much will be saved if one student decided not to go on the trip?

Our Answer

If 30 students register, three adults must accompany them, for a total of 33 passengers. There is no need to rent an additional bus.
Trip costs include the cost of the bus ($150), plus the cost of 33 admissions (33 x $8 = $264), for a total of $414.
Cancellation by one student saves $8 (the price of the museum admission). Travel costs are unaffected.
For the trip in question 11, little Johnny's parents forgot to register their son on time, but little Johnny really wants to go to the museum!
What is the marginal cost of adding one student to the group (assuming that all 30 students who signed up actually go on the trip)?
Our Answer
Adding one student to the 30 increases the number of passengers to 35 (one additional student, plus one additional adult). It is now necessary to

rent an additional bus ($90), and

purchase two additional museum admissions (2 x $8).

Therefore, the marginal cost of adding one student is $106.
Suppose that you are conducting a cost analysis with the purpose of estimating the cost of investigating the contact of TB patients (i.e., identifying, screening, and appropriately treating the contacts).
A sample of contacts has been selected from public health departments' files throughout the country. Researchers have collected the information below.
- Labor and testing costs are, on average, $115 per contact. However, sites reported costs as high as $220 and as low as $30.
- The sample yields an average infection rate of 15% among contacts. However, a closer look at the data indicates that some contacts (e.g., foreignborn, homeless, or immunosuppressed persons) are at higher risk for tuberculosis infection (up to 30% higher).
- The average cost of treating an infected contact is $500.
- On average, 55% of infected contacts are placed on preventive therapy. However, national guidelines for tuberculosis-control programs include a target goal of 75%.
Calculate the average cost per contact investigated of conducting a contact investigation for a cohort of 10,000 contacts.

Our Answer

The average cost per contact investigated is

Average cost per contact investigated = Total costs / Number of contacts investigated

where

Total costs = Investigation costs + Treatment costs

Investigation costs = Cost of investigating a contact x Number of contacts investigated

Treatment costs = Cost of treating an infected contact x Number of treated contacts

Number of treated contacts = Number of infected contacts x Likelihood of receiving treatment

Number of infected contacts = Number of contacts investigated x Likelihood that a contact is infected

substituting:

Number of infected contacts = 10,000 x 0.15 = 1,500

Number of treated contacts = 1,500 x 0.55 = 825

Treatment costs = $500 x 825 = $412,500

Investigation costs = $115 x 10,000 = $1,150,000

Total costs = $1,150,000 + $412,500 = $1,562,500

Average cost per contact investigated = $1,562,500 / 10,000 = $156.25
For question 13, how could the researchers account for the uncertainty in their data and assumptions?

Our Answer

The uncertainty in the information available can be factored into the analysis by conducting a sensitivity analysis.
For question 13, which parameters could be varied in a sensitivity analysis? Which ones could be varied in a threshold analysis?

Our Answer

A sensitivity analysis should be conducted around labor/testing costs, the infection rate among the contacts investigated, and the treatment rate. All three parameters could be varied in sensitivity analysis (one-way or multiway) or in threshold analyses.
Labor/testing costs could be varied in a best-case/worst-case scenario, by using the high and low cost estimates available. Labor/testing costs could also be varied in a threshold analysis, from the low to the high value, to assess how total and average costs change as labor/testing costs increase.
In the same way, the infection rate could be varied to a higher value (e.g., 30%). In a threshold analysis, the infection rate could be varied between 15% and the higher value to assess how total and average costs change as prevalence increases.
If the researchers suspect the actual infection rate to be higher than 15%, they would choose to increase the infection rate in the sensitivity analysis. If they do not know whether the actual infection rate is lower or higher than 15%, the researchers would explore both a higher and lower prevalence in the sensitivity/threshold analyses.
The treatment rate could be varied to 75% in a sensitivity analysis to assess the impact of implementing guidelines on total/average costs. Conducting a threshold analysis around treatment rates would reveal how total and average cost might change as the program progressively works toward meeting treatment standards.
For question 13, conduct a one-way sensitivity analysis around labor costs. Which alternative values could you use for labor? Do variations in labor costs have a significant impact on the cost analysis results?

Our Answer

In a one-way sensitivity analysis, labor costs could be increased to $220 and decreased to $30 to reflect the information available about this intervention.
If

Labor/testing cost = $30 per contact investigated (best-case scenario)

then

Total costs = ( 10,000 x $30 ) + $412,500 = $300,000 + $412,500 = $712,500

Average cost = $712,500 / 10,000 = $71.25

If

Labor/testing cost = $220 per contact investigated (worst-case scenario)

then

Total costs = ( 10,000 x $220 ) + $412,500 = $2,200,000 + $412,500 = $2,612,500

Average cost = $2,612,500 / 10,000 = $261.25

Labor/testing costs do have a strong impact on the cost analysis results: the worst-case scenario results are almost 4 times as high as the best-case scenario results.
For question 13, conduct a multiway sensitivity analysis around infection prevalence and the probability of receiving treatment.

Our Answer

This multiway sensitivity analysis explores the impact that a higher infection rate coupled with a higher treatment rate would have on cost results.

Total costs = ( 10,000 x $115 ) + ( 10,000 x 0.3 x 0.75 x $500 )

= $1,150,000 + $1,125,000

= $2,275,000

Average cost = $2,275,000 / 10,000 = $227.50 per contact investigated

Cost of Illness

The Cost of Illness (COI) is defined as the value of the resources that are expended or foregone as a result of a health problem. The COI includes health sector costs, the value of lost productivity by the patient (indirect cost), and the cost of pain and suffering (intangible costs).

Why Should We Calculate the COI?

The objective of health policy decisionmakers is to improve the health status of society. Public health research and surveillance data (e.g., epidemiological studies) help determine the nation's current health profile and problems. They also identify the effectiveness of available technologies in eliminating these problems.

To make informed choices concerning which health problems to address and what interventions to use to alleviate them, we need to know the economic burden imposed by the various health problems. The COI provides a monetary estimate for the economic burden of diseases.

The majority of COI studies estimate the medical expenses and dollars of employment compensation that are foregone as a result of illnesses or premature death. This information provides us with estimated magnitudes of economic flows associated with government programs. With this knowledge we are able to assess the economic impacts of various health problems.

COI studies allow us to determine the amount of money that we spend on an illness and to compare it with what we spend on the interventions that decrease or eliminate the problems. This determination helps us answer the question "Is the intervention worth it?". By combining this data with information from the previous chapter (Cost of the Intervention or Program

), we can estimate

how much the intervention costs,
how much the illness costs before (or without) the intervention, and
how much the illness costs after (or with) the intervention.

Other reasons for estimating COI are similar to those discussed in the Introduction

and Cost of the Intervention or Program

chapters of this cost analysis tutorial.

Determining COI

We can follow the same systematic steps below to determine the COI as we did in estimating the cost of an intervention

Frame the cost analysis.
Develop a cost inventory.
Measure resource use.
Calculate cost analysis results.

Framing the Cost Analysis

The first step in framing a study involves defining the problem and adopting a research strategy. Each component of framing a study is discussed in detail in the previous chapter; the same considerations are relevant for framing a COI study.

Specifically for COI analysis, we have to choose a time frame, taking into account the characteristic duration of the illness in question. Some acute illnesses (e.g., the common cold) have a short duration. Other illnesses (e.g., HIV or tuberculosis) have durations that often extend over long periods.

Developing a Cost Inventory

The perspective we choose dictates what costs to include. In the COI studies, we use the direct, indirect, and intangible classification schemes described in the Classification Systems

section in the previous chapter.

Direct Costs

Direct costs of illness are expenditures for medical goods and services (e.g., medications, doctor visits, and hospitalization). Often direct costs are further classified as direct medical and direct nonmedical costs, depending on whether or not the resources have been expended directly in production of a treatment.

For instance, direct medical costs of end-state renal disease (ESRD) include the cost of treating ESRD and its co-morbidities (e.g., hypertension, electrolyte imbalance, anemia, dialysis complications, and side effects).

The direct nonmedical costs of ESRD include costs for such items as transportation to clinics and home modifications for in-house dialysis machines.

If the perspective of our study is societal, dividing costs into those borne by the health sector and those borne by the household is useful. The general categories of costs in each division are reflected in the table below.

Health sector costs	Family costs
Hospitalization	Out-of-pocket payments (user fees) for hospitals and drugs
Medication	Medication
Emergency (ambulance) transportation and care	Transportation of the patient and family
Outpatient and primary clinic	Costs for taking care of dependents
	Modifications in home as a result of illness

User fees are out-of-pocket expenses for patients that certain public health systems require for their service. Double counting these user fees is an easy mistake to make. These fees must be accounted for either in the family cost category or in the health sector category, but not in both.

Indirect Costs

Indirect costs or productivity losses are the labor earnings that are forgone as a result of an adverse health outcome. The decreased productivity can be a result of illness, death, side effects, or time spent receiving treatment. Indirect costs include lost earnings and productivity of both patients and the family members who take care of them. For some diseases with premature death, the indirect cost is the loss in potential wages and benefits. Indirect costs associated with premature death might be very high.

Economists consider health to be a human capital investment. According to this approach, the value of health is measured in terms of its contribution to production activity and national income. By following the methods developed in the human capital approach, we can measure indirect costs by using data from the labor markets. Earnings lost because of time spent while ill or receiving medical treatments are used to estimate the value of time lost. Examples of indirect illness costs include

the value of time spent when unable to work as productively because of an illness or side effect,
earnings lost while traveling to health-care facilities, and
productivity losses associated with caregiver time.

Intangible Costs

The intangible cost components of illness are usually substantial, and in many cases, might dominate the policy agenda. Examples include

disfigurement (e.g., breast cancer with surgery),
functional limitations (e.g., paralysis from polio),
pain (e.g., rheumatoid arthritis or bone metastasis), or
fear (e.g., HIV, rabies, or bovine spongiform encephalopathy [BSE]).

One approach to estimating the intangible costs is through willingness-to-pay (WTP) studies. However, WTP is a complex method requiring specialized expertise in designing and implementing surveys.

Because of 1) complexities involved with implementing WTP studies and 2) unresolved theoretical controversies in measuring intangible costs, the majority of economic evaluations include only their qualitative discussion.

Estimating Resource Use and Calculating Results

Because of data and methodological limitations, the majority of COI studies in the literature estimate only a part of the full economic costs of illness represented by direct, indirect, and intangible costs. A simplified approach is documented below.

COI

Number of episodes

(

Direct cost per episode

Indirect cost per episode

)

where

Direct cost per episode

Direct outpatient costs

Direct inpatient costs

Direct homecare costs

Indirect cost per episode

Value of production

(

Production lost because of illness

Production lost because of caregiving

)

We can generate multiple summary measures to analyze costs.

Total cost: resources expended for all patients with the illness.
Average costs: cost per case of illness.
Annual cost: The COI per year.

Case Study: Hepatitis A Outbreak — Denver, Colorado, 1992

Context

Outbreak:	During November–December 1992, 44 cases of hepatitis A associated with a catering facility were reported to the Colorado Department of Public Health and Environment. The 44 cases included 10 employees from the catering company, and 34 persons who attended parties catered by the company. Approximately 5,000 persons were considered potentially exposed to hepatitis A by attending functions at which the food was prepared by the 10 infected food handlers.
Intervention:	The Colorado Department of Public Health and Environment and the Tri-County Health Department notified party attendees of their potential exposure by contacting party hosts and conducting a news conference. Approximately 16,000 people received immune globulin prophylaxis.
Objective:	To estimate the cost of the disease-control program and the COI.

Source of This Study

Dalton, CB, Haddix, Anne, et al., The Cost of a Food-Borne Outbreak of Hepatitis A in Denver, Colorado. Arch Intern Med 1996:156:1013–16

Methods

Study population:	Food handlers at catering facilities and residents of the metropolitan Denver area who had used the services of the catering facility.
Study design:	Retrospective program cost and COI analysis.
Study perspective:	Societal.

Calculating Costs

Societal Costs

The total cost to society estimated in this study comprises multiple different costs.

Disease-Control Costs

The components of disease-control costs were estimated from 1990 data on actual payments for services classified by diagnosis related group codes obtained from Blue Cross/Blue Shield. These costs are summarized below.

Health Department Costs

Health department costs, which are estimated on the basis of diary and payroll records, are considered to consist solely of personnel costs. Information is collected from each agency for each employee involved in work related to the outbreak during December 1992 and January 1993.

Total personnel costs were calculated to include the hourly wage, benefits, and insurance and workers compensation premium of each employee.

Costs of Testing Suspected Hepatitis A Cases

The metropolitan Denver hospitals and commercial laboratories furnished counts of the hepatitis A serologic tests for total immunoglobulin and IgM (anti-hepatitis A virus) performed during November 1992–January 1993.

The excess number of tests performed in January 1993, compared with the average during November–December 1992, was attributed to the outbreak.

The cost of evaluating a suspected case, $81.28, was based on an average payment of $30.28 for the serologic test and a physician fee of $51.

Costs of Immune Globulin Administration

Administrative costs were determined for

HMOs: The cost of the injection, based on average payment data from 13 hospitals, was an estimated $34.
Health Departments: Four local health departments were contacted to estimate
- globulin cost: $2, and
- personnel time cost: $16.

Business Costs

Business costs are estimated to include only the cost of the food discarded by the catering company. The catering company's decreased profit was not included as a cost to society; it was assumed that other catering companies would have acquired the lost business.

COI

COI is considered to consist of the two components below.

Medical costs: Direct medical charges are used as a proxy for cost.
Productivity losses: For patients and their relatives, productivity losses are estimated by multiplying the cost of 1 day of lost productivity by the mean number of days lost from performing productive work as a result of the illness.
Productivity Loss Detail
Productivity losses for 43 persons who developed hepatitis A were based on data from patients with acute hepatitis A enrolled in the Sentinel Counties Cost Study (CDC, Hepatitis Branch, unpublished data, 1995).
The Sentinel Counties Cost Study assessed the mean amount of time lost from performing routine productive duties by patients and their relatives because of hepatitis A. This assessment was made based on 50 population-based reports of hepatitis A in the county of Denver in 1991.
- The median duration of absence from work was 12.5 days (range: 6–25 days) for hospitalized cases and 7 days (range: 1–23 days) for outpatient cases.
- The cost of a day of lost productivity was calculated on the basis of average national earnings and the imputed value of household work, adjusted by age and sex. Its value was an estimated $94; this value included data for nonemployed persons and was based on a 40-hour, 5-day working week.
- The cost of travel and productivity losses for persons receiving immune globulin and serologic testing and the cost of caretakers' time was excluded from this analysis.

Data Collected

Data was collected for the following items:

health department, HMO, hospital, and catering company records,
salaries and benefits of personnel at county departments of health and personnel time devoted to work related to the outbreak,
number of serologic tests and immune globulin injections performed in 13 hospitals and two commercial laboratories,
data from1990 on actual payments for services from Blue Cross/Blue Shield HMOs, and
cost and revenue data from the catering company.

Results: COI Estimates

Cost category	Quantity	Unit cost ($)	Subtotal ($)	Total ($)
Disease-Control costs
Health department personnel time	2,777	38/hour*	105,699
Serologic tests and physician fees	1,639	81.28	133,218
Immune globulin injections
Health department clinics	3,794	6.7	25,431
HMOs/hospitals	12,499	34.00	424,966
Total: Disease control			689,314	689,314
Business losses
Discarded food			45,000	45,000
Illness costs for cases
Direct medical
Outpatient	41		31,092
Hospitalized	2		14,972
Total: Direct medical			46,064	46,064
Productivity losses
Outpatient	41 x 7**	94/day	26,978
Hospitalized	2 x 12.5**	94/day	2,350
Total: Productivity losses			29,328	29,328
Total cost to society				809,706

*Mean personnel cost per hour (salary, benefits, workers compensation, and medical insurance)
**Person-days

Conclusion

The medical costs and productivity losses composed only approximately 9% of the total cost of the outbreak. The high cost of foodborne outbreaks is an important factor that should be considered in economic evaluation studies of vaccination programs for food handlers.

Advantages and Shortcomings of the COI Approach

The apparent ease of estimation of direct and indirect costs of illness accounts for the widespread use of the COI approach. However, the following factors make the estimation complex and highlight limitations of certain uses of COI estimates.

No uniform COI template exists.
Data are usually insufficient and inexact.
Using CCRs (described in Using Cost-To-Charge Ratios [CCRs]) to adjust the charges for medical services provides only approximate estimates of true economic costs for direct expenses.
Making an accurate estimate of productivity losses is difficult. Wages and benefits are used to estimate the forgone earnings for working patients and household members.
Making an accurate estimate of the cost of nonmarket goods and services is more difficult than doing so for productivity losses.
COI estimates are often used as a measure of the monetized benefits of public health programs. The total of the costs that are avoided represents the value of program benefits. However, COI estimates do not provide correct measures of the social value of program benefits.
Persons incur losses in their welfare when they pay for medical expenses by cutting their consumption and forgoing the utility that this consumption provides. In contrast, these direct expenditures stimulate economic activity and produce welfare in health care and other sectors of the economy. Therefore, the direct costs of illness do not represent the social costs accurately.
COI estimates are often used as measures of disease severity. However, COI estimates provide a measure of the economic consequences of an illness, not of disease severity. The direct costs of an illness reflect the types of medical interventions currently available, whereas indirect costs measure the affected population's education level, skill level, income, sick-leave benefits, and insurance coverage.

Despite these shortcomings, the COI approach provides useful information regarding economic flows associated with an adverse health outcome and is a useful economic tool to guide resource allocation decisions.

Test Your Understanding

Please enter your answer to each question before you click on "Our Answer".

Suppose you are conducting from a societal perspective a COI analysis to estimate the economic burden of influenza in the United States. You are provided with the information below from a representative sample.
- Average direct cost of treating each case is $86 (range: $21–$140).
- Average indirect cost for treating each case is $190 (range: $ 44–$560).
- The sample yields an incidence rate of 7.5%. However, other studies indicate that incidence rates are in the range of 4%–12%.
What might be some of the direct cost components of influenza in the United States?
Our Answer
Direct costs include

physician services costs,

diagnostic/laboratory testing costs,

vaccination costs,

physician services costs in emergency departments,

prescription drug costs,

over-the-counter drug costs, and

costs for treating complications.
What might be some of the indirect costs for influenza in the United States?
Our Answer
Indirect costs include

value of productivity losses from morbidity,

value of productivity losses from premature mortality, and

value of caregivers' productivity losses.
Will the results of a COI study that is based on estimating direct and indirect cost components reflect the full economic burden of influenza in the United States?
If not, what is the omitted component?

Our Answer

No. The results of a COI study based on estimating only direct and indirect costs will not reflect the full economic burden of influenza in the United States.
The intangible costs are an integral part of the COI estimates, although they are difficult to quantify and often are discussed qualitatively in COI analyses.
Assuming that the population of the United States is 280 million, calculate the COI for influenza by using the following formula:

COI = Number of cases x ( Average direct cost per case + Average indirect cost per case )

where

Number of cases = Population x Disease Incidence rate

Our Answer

Number of cases = Population x Disease Incidence rate

= 280,000,000 x 0.075

= 21,000,000

COI = Number of cases x ( Average direct cost per case + Average indirect cost per case )

= 21,000,000 x ( $86 + $190 )

= $5,796,000,000
How would you account for the uncertainty in the data?

Our Answer

The uncertainty in the available data can be factored into the analysis by conducting a sensitivity analysis.
Which parameters would you vary in a sensitivity analysis?

Our Answer

A sensitivity analysis should be conducted around direct costs, indirect costs, and the incidence rate. All three parameters can be varied in a sensitivity analysis, one-way or multiway.
As we discussed in the previous chapter, conducting cost analysis inevitably involves uncertainties regarding some parameters. The sensitivity analyses reveal the impact of these uncertainties by calculating the changes in analysis results when one or multiple study parameters are varied.
Recalculate the COI by using the minimum and maximum values for direct cost per case.

Our Answer

In a one-way sensitivity analysis, direct costs per case could be increased to $140 and decreased to $21.

COI = 21,000,000 x ( $140 + $190 )

= $6,930,000,000

COI = 21,000,000 x ( $21 + $190 )

= $4,431,000,000
Recalculate the COI using the maximum values for infection prevalence and direct and indirect costs per case.

Our Answer

This multiway sensitivity analysis below explores the impact that a higher incidence rate as well as higher direct and indirect costs per case would have on cost analysis results.

Number of cases = 280,000,000 x 0.12

= 33,600,000

COI = 33,600,000 x ( $140 + $560 )

= $23,520,000,000

Adjusting Costs

Costs and outcomes of health programs usually occur at different points in time. We have to adjust the values from different periods to obtain correct final results. Economists have developed methods that account for this differential in timing and make them comparable.

Discounting Future Costs

Persons have time preferences for events: they would rather receive benefits now than in the future and bear costs later. For example, if offered the choice between receiving $100 today or the same amount in 10 years, people would typically prefer to receive $100 immediately. If we are given $100 today, we can put that money to use and derive benefits immediately.

We could also invest the $100 and earn interest on it. The interest earned is the reward we require to delay our consumption and a concrete indicator of time preference. Similarly, the interest we pay on our credit card balance is the extra value we are willing to pay for obtaining a good or a service immediately, instead of waiting until we have accumulated enough money to pay for the item in full.

The premium placed on benefits today versus the future is reflected in the rate at which a person is willing to exchange the present for future costs and benefits. This quantitative measure of time preference is called the discount rate. Discounting involves applying a discount rate to adjust future costs and benefits to their present values. Discounting future costs makes it possible to

evaluate future costs from the perspective of the moment in time in which the decision to allocate funds must be made, and
compare programs and interventions with costs that are spread out differently over time. Some interventions might be more costly up front, whereas others might require that more resources be expended in the long term.

What Is the Appropriate Discount Rate?

The perspective of the study determines what discount rate to apply. If we are interested in the patient's perspective we must apply an individual discount rate.

Determining the discount rate for a patient depends on 1) whether the person has a short- or long-term view of life and 2) the level of certainty of his or her future.

A discount rate of 0% indicates no distinction between present and future costs and benefits.

A person suffering from a fatal disease might have a very high discount rate because the future that he faces is uncertain.

We must use a private sector discount rate if we are conducting a study from the perspective of the industry sector or of private organizations (e.g., managed-care organizations). Private sector discount rates depend on factors (e.g., business conditions) that the companies face.

For example, for a health plan in which membership is fluid, the company will have a higher discount rate reflecting its preference to avert costs in the present rather than in the future.

The societal perspective requires the use of the social discount rate. The social discount rate represents the collective willingness to exchange the present for future benefits.

Factors (e.g., individuals' attitudes toward society and consideration of children as part of future society) determine the social discount rate.

CDC currently recommends that a 3% social discount rate be used in analyses that require adjusting future costs and benefits of public health interventions, programs, and policies. This rate can be varied from 0% to 10% in sensitivity analyses.

How Do We Discount Future Costs?

Future costs can be discounted by using the following formula:

Present value

Future value

Discount factor

where

Discount factor	=	1 / (1 + r)ⁿ
r	=	discount rate
n	=	year

You can calculate the present value from these formulas. But raising (1 + r) to the nth power requires

patience,
a hand-held calculator with an exponential capability, or
the Windows calculator in scientific view.

Two additional ways that are easier and faster to use are below.

1. Use This Present Value Spreadsheet Calculator.

Calculate present values with this spreadsheet. We have filled it with some sample values. Enter your values and click the Calculate button.

2. Use Precalculated Discount Factors.

As you saw earlier, you can calculate the present value from the future value and the discount factor with the following formula:

Present value

Future value

Discount factor

To obtain the discount factor you can use the Discount Factor Table

in Appendix C. (This window will stay open.)

Example 1: Discounting Future Costs

Project A costs $100 in Year 1 to implement. Project B costs $100 in Year 20.

Question: Which of the Two Programs Is Less Costly?

Which project is less costly in its present value, given a social discount rate of 3%?

Answer: Use Our Spreadsheet Calculator.

When you use the spreadsheet calculator, follow these steps:

Set up a table like the one below and fill in the Problem data columns with the given data for the problem.
Enter the values into our Spreadsheet Calculator from the Project A row of the table below. Enter the resulting present value into the present value column of the table.
Repeat step 2 for the Project B row.
Compare the present values in the two rows.

Project	Problem data			Results
	Discount rate (%)	Year	Future value ($)	Present value ($)	Less costly
A	5	1	100	97.07
B	5	20	100	55.37

Project B is less costly than Project A.

Answer: Use a Calculator or the Discount Factor Table.

The formulas and results for each of the projects are in this table. Project B is less costly than Project A.

Project	Present value
	PV formula	Discount factor table	Less costly
A	$100 x (1 / (1 + 0.03) ¹) = $97.09	$100 x 0.9709 = $97.09
B	$100 x (1 / (1 + 0.03) ²⁰) = $55.37	$100 x 0.5537 = $55.37

Example 2: Discounting Future Costs

Annual costs for Project A are

Year 1 = $100,
Year 2 = $200, and
Year 5 = $300.

Question: What Are the Total Program Costs?

What is the present value of the total program costs, if the social discount rate is 5%?

Answer: Use a Discounting Calculator.

This spreadsheet calculates the annual costs for the example. Try it using your own values. Enter them and click the Calculate button.

Why Are We Discounting the First Year?

In the previous examples, we assumed that the present value is calculated for the beginning of Year 1 and that the costs for that first year and for subsequent years were incurred at the ends of the respective years.

Therefore, for the first year, a full 12 months elapses before the first costs are incurred. So we discount the Year 1 costs. Similarly, for costs in subsequent years — if the costs occur at the ends of the years, we discount the final year fully, as well.

If the present value will be calculated based on the same time that the first year costs accrue, then the costs for Year 1 cannot be considered future costs and should not be discounted. And if costs occurring in Year n occur at the beginning of Year n, we should discount those costs only for Years (n – 1).

Either method of discounting is appropriate (although the results will differ by a percentage equal to the discount rate), as long as all costs are discounted consistently and systematically. The example below illustrates how results vary with the discounting method used.

Example: Effect of Starting Discounting in the First Year

		Costs incurred at end of year		Costs incurred at beginning of year
		First year is discounted		First year is not discounted
Year	Cost	Calculation	Value	Calculation	Value
1	$100	$100 / (1 + 0.05)¹ = $200 x 0.9524	$95.24	$100 / (1 + 0.05)⁰ = $100 x 1	$100.00
2	$200	$200 / (1 + 0.05)² = $200 x 0.9070	$181.40	$200 / (1 + 0.05)¹ = $200 x 0.9524	$190.48
5	$300	$300 / (1 + 0.05)⁵ = $300 x 0.7835	$235.05	$200 / (1 + 0.05)⁴ = $300 x 0.8227	$246.81
Total cost			$511.69		$537.29

The difference between the two total cost values ($537.29 – 511.69 = $25.60) should represent 5% (the discount rate) of the total cost value for the Year 1 discounted case. Indeed, $25.60 divided by $511.69 is 0.05.

Adjusting for Inflation

What Is Inflation?

Inflation is a persistent and appreciable increase in the general price level that occurs over time. This increase in general price level decreases the purchasing power of each unit of currency (e.g., $1). Because of inflation, $1 is worth less (in terms of what it can purchase) this year than last year.

Why Do We Need To Adjust for Inflation in Cost Analysis?

Cost data are often collected from different years. Inflation renders direct comparison of unadjusted cost data inaccurate.

To make costs from different years comparable, we have to standardize all costs to the same base year. Because we want our cost analysis results to be as up-to-date as possible, the most recent year for which data are available is usually chosen as the base year. Costs can be adjusted to the same base year using the Consumer Price Index (CPI).

CPI tracks the change in price of a fixed "market basket" of goods and services typically consumed by an average family in the United States. The Bureau of Labor Statistics (BLS), a federal government agency, monitors the evolution of price levels (for consumer goods, commodities, services, salaries, and wages) in the United States.

CPI is presented in the form of an index: it is expressed in terms of change relative to a reference point. The reference point currently used by the BLS is 1983–1984, which means that the value of the index for that year was set at 100. Index values for years before and after 1983–1984 can be expressed in relation to that reference point.

For example, the index value for 1960 is 29.6, which means that in 1960, prices (as measured by the CPI) were 70.4% lower than they were in the reference year (1983–1984).

Current and historical estimates of CPI as well as information regarding the composition and computation of the index are available on the BLS Internet home page: http://www.bls.gov/cpi/

Updates are published on a monthly basis.

Click this link to see the Consumer Price Index Table

in Appendix B. (This window will stay open.)

CPI includes a medical care component that can be used as a separate index to adjust medical prices. The following table lists the items included in the medical care component:

CPI — Medical Care Component

CPI — Medical Care Component
Medical care commodities	Medical care services
Medical care commodities	Professional medical services	Hospital and related services	Health insurance
Prescription drugs Nonprescription drugs Nonprescription medical equipment and supplies	Physician services Dental services Eye care services Services by other medical professionals	Inpatient services Outpatient services Nursing home services	Out-of-pocket insurance premiums

Using the medical care component of CPI to adjust prices in a cost analysis of a health intervention can be controversial.

Some researchers argue that the evolution of the level of medical care prices over time is not caused by inflation as much as it is caused by changes in the nature of the services themselves (changes caused, in particular, by technological innovations).

When you are in doubt, use the all-items component of the CPI, which is preferable.

How Do We Adjust for Inflation?

Unadjusted prices are referred to as "nominal prices," "nominal dollars," "current dollars," or "current prices". After these unadjusted prices are adjusted for inflation, they are referred to as "constant dollars," "constant prices," "real dollars," or "real prices."

Prices can be adjusted for inflation by using the following equation:

Y_B

Y_P

(

CPI_B

CPI_P

)

where

Y_B	=	base year value
Y_P	=	past year value
CPI_B	=	CPI value of base year
CPI_P	=	CPI value of past year

An Example: Adjusting Prices for Inflation

In conducting a cost analysis, you decide that program costs will be reported in 1999 dollars. Supply costs were collected for 1997 and therefore must be converted to the base year, 1999.

Use the Consumer Price Index Table

in Appendix B for the CPI values. (This window will stay open.)

CPI₁₉₉₇	=	All-items component of the CPI for 1997	=	160.5
CPI₁₉₉₉	All-items component of the CPI for 1999	=	166.6

To adjust the 1997 supply cost of $15.00 to the 1999 price, use the following equations

Price₁₉₉₉	=	Price₁₉₉₇	x	(CPI₁₉₉₉	/	CPI₁₉₉₇)
Price₁₉₉₉	=	$15.00	x	(166.6	/	160.5)
Price₁₉₉₉	=	$15.00	x	1.038
Price₁₉₉₉	=	$15.57

Adjusting Earnings to Base Year Monetary Units

We must also adjust previous year earnings to the base year to be able to make consistent comparisons. The appropriate index to use for this adjustment is the estimated annual increase in average hourly earnings, which reported annually in the March issue of Employment and Earnings from BLS.

The equation that you should use for adjusting earnings is essentially the same as the one for adjusting for inflation:

I_B

I_P

(

W_B

W_P

)

where

I_B	=	income in base year
I_P	=	income in the past year
W_B	=	average hourly wage in base year
W_P	=	average hourly wage in the past year

Example: Earnings Adjustment

The cost analysis has revealed the productivity losses caused by an influenza outbreak in 1990, which totaled $125 million. We want to report the results in 1993 base year dollars. The average hourly earnings for 1990 and 1993 were $10.01 and $10.83, respectively. The adjusted productivity loss for 1993 will be

Productivity Loss₁₉₉₃

$125 (10.83/10.01)

$135.24 Million

Annuitizing Capital Costs

What are Capital Costs?

Capital costs represent expenditures on resources like equipment, buildings, and land. They are usually purchased once at the beginning of the program and have useful lives greater than 1 year.

Resources with a useful life of less than 1 year that are purchased repeatedly over the lifespan of the program or intervention are called recurrent or operating costs. Drugs, office supplies, and gasoline are examples of operating costs.

Why Should Capital Costs Be Annuitized?

Annuitizing involves determining an annual value of capital item for the life of the resource. Capital resources provide useful services over their lifespan. When calculating costs we have to take into account that this services accrue over various years of the program. Annuitizing allows us to match the services capital resources provide with their costs.

Assigning the entire purchase cost to only the purchase year would overestimate that year's costs and underestimate future periods' costs. Annuitizing spreads the capital costs over the useful life of resources and provides more accurate estimates of true resource use.

How Do We Annuitize Capital Costs?

Capital costs can be annuitized in three steps.

Step 1: Calculate the Present Value (PV) of the Capital Item's Scrap Value.

We base the calculation on the year that the good is scrapped and on the discount rate.

SV x 1 / (1 + r)ⁿ

where

SV	=	Scrap value
r	=	Discount rate
n	=	Length of the item's useful life

Note:

In this step, we are simply applying the discounting formula presented earlier in this tutorial to the scrap value of the capital item. The discounting factor table can be used to perform this step.

Step 2: Calculate the Item's Annuity Factor (A).

( 1 / r ) - ( 1 / ( r ( 1 + r )ⁿ) )

where

r	=	Discount rate
n	=	Length of the item's useful life

Click this link to see the Annuity Factor Table

in Appendix D. (This window will stay open.)

To identify the appropriate annuity factor from the table, locate the

column that corresponds to the discount rate used in the cost analysis;
row that corresponds to the number of years of the item's useful life; and
appropriate annuity factor, which will be at the intersection of the row and column.

For example, the annuity factor for a discount rate of 3% and a useful life of 5 years is 4.5797.

Step 3: Calculate the Item's Equivalent Annual Cost (EAC).

EAC

( PC - PV ) / A

where

PC	=	Purchase/Replacement cost of the capital item
PV	=	Present value of scrap value (from Step 1)
A	=	Annuity factor (from Step 2)
n	=	Length of the item's useful life

An Example: Annuitizing Capital Costs

A building is purchased for $200,000 in Year 1 of a program. Let us assume that the

useful life of the building is 10 years,
building can be sold after 10 years for $50,000 (scrap value), and
social discount rate is 3% per year.

Step 1: Calculate the Present Value of the Scrap Value (PV)

( $50,000 x 0.7441 )

$37,205

Step 2: Calculate the Annuity Factor (A)

1 / 0.03 - 1 / ( 0.03 ( 1 + 0.03 )¹⁰)

8.5302

Alternatively, you can obtain the annuity factor from the Annuity Factor Table

in Appendix D. The factor is at the intersection of the 3% discount rate column and 10 years useful life row.

Step 3: Calculate the Equivalent Annual Cost (EAC)

EAC

( 200,000 - 37,205 ) / 8.5302

$19,085

This equivalent annual cost of $19,085 can now be used as an estimate for the average annual cost of the building. Average annual costs for the program can now be calculated as

	Year 1	Year 2	Year 3	Year 4
Capital costs
Building	$19,085	$19,085	$19,085	$19,085
Recurring costs
Personnel	$100,000	$100,000	$100,000	$100,000
Supplies	$1,000	$1,000	$1,000	$1,000
Total costs	$120,085	$120,085	$120,085	$120,085

Test Your Understanding

Please enter your answer to each question before you click on "Our Answer".

You want to report the results of a cost analysis in 1999 dollars. However, the only data that you were able to collect regarding supply costs was for 1998. What should you do to use 1998 data in your cost analysis?

Our Answer

The 1998 data can be used in a cost analysis in 1999 dollars after being adjusted for inflation.
The cost of an item in 1998 dollars was $23.
1. What is the value of the all-items component of CPI for 1998?
  
  Our Answer
  
  The value for 1998 is 163.
2. What is the value of the all-items component of CPI for 1999?
  
  Our Answer
  
  The value for 1999 is 166.6.
3. By what percentage has the general price level increased from 1998 to 1999?
  
  Our Answer
  
  From 1998 to 1999:
  
  General price level increase = (166.6 – 163) / 163
  
  = 3.6 / 163
  
  = 0.022
  
  = 2.2%
4. How much does the item cost in 1999 dollars?
  
  Our Answer
  
  If the item was $23 in 1998, its cost in 1999 dollars is
  
  Cost1999 = Price1998 x (CPI1999 / CPI1998)
  
  = $23 x (166.6 / 163)
  
  = $23 x 1.022
  
  = $23.50
5. What assumptions are you making when you use the item's adjusted value in your cost analysis?
  
  Our Answer
  
  You assume that the cost of this item has changed at the same rate as CPI.
Program A will cost $100,000 to implement in 2001.
Projected costs for Program B, which will be implemented in 2005, are $120,000.
Which program is more costly in terms of its present value (assuming that 2001 is the current year)?
Our Answers
Future costs incurred at different points in time must be discounted before they can be compared. We assume a discount rate of 3%, but other discount rates would be acceptable.
Two alternatives are available: we can assume that 2001 is either Year 0 or Year 1.

Year 0

If 2001 is Year 0 (and 2005 is Year 4):

The cost of Program A is

CostA = $100,000

The cost of Program B is

CostB = $120,000 x 1 / (1+0.03)⁴

= $120,000 x 0.8855

= $106,620

Year 1

If 2001 is Year 1 (and 2005 is Year 5):

The cost of Program A is

CostA = $100,000 x 1 / (1+0.03)¹

= $100,000 x 0.9709

= $97,090

The cost of Program B is

CostB = $120,000 x 1 / (1 + 0.03)⁵

= $120,000 x 0.8626

= $103,512

Both alternatives lead to the same conclusion:

Program A is less costly than Program B.
The annual cost of a 5-year intervention to remove lead paint from old inner-city apartments is expected to be as follows:

Year 1 Year 2 Year 3 Year 4 Year 5

$100,000 $125,000 $150,000 $200,000 $125,000

What is the total cost of the intervention in terms of its present value?

Our Answers

Here again, we can place ourselves in Year 0 or in Year 1 to start the discounting.
Year 0

Starting in Year 0, Year 1 costs are discounted.
The total present value of the program is

= $100,000 x 0.9709 + $125,000 x 0.9426 + $150,000 x 0.9151 +

$200,000 x 0.8885 + $125,000 x 0.8626

= $97,090 + $117,825 + $137,265 + $177,700 + $107,825

= $637,705

Year 1

Starting in Year 1, the Year 1 costs are not discounted.
The total present value of the program is

= $100,000 + $125,000 x 0.9709 + $150,000 x 0.9426 +

$200,000 x 0.9151 + $125,000 x 0.8885

= $100,000 + $121,363 + $141,390 + $183,020 + $111,063

= $656,836
You have been asked to calculate the total cost of a childhood immunization program over a 5-year period.
1. Should you discount future costs?
  
  Our Answer
  
  Future costs need to be discounted to be summed up.
2. Should you annuitize capital costs?
  
  Our Answer
  
  Capital costs only need to be annuitized if you want to calculate average annual costs. If you are only interested in total program costs, capital costs do not need to be annuitized.
A community program that delivers meals to homes of persons with AIDS bought a new van for $55,000. The program director plans to use the van for 10 years and then sell it for its blue book value of $5,000.
If we assume a discount rate of 5%, what is the annual cost of the van?
Our Answer
The van's purchase price is $55,000; its useful life is 10 years; and its scrap value is $5,000. The discount rate is 5%. Below are the steps that should be followed:

Calculate the present value of the scrap value.

PV of scrap value = $5,000 x 1 / (1 + 0.05)¹⁰

= $5,000 x 0.6139

= $3069

Identify the Annuity factor.

For a 5% discount rate and a useful life of 10 years, the Annuity factor is 7.2717

Calculate the equivalent annual cost.

Annual cost = ( Purchase price - PV of scrap value ) / Annuity factor

Annual cost = ($55,000 – $3069.50) / 7.2717

= $7,141

Total costs	=	( 10,000 x $115 )	+	( 10,000	x	0.3	x	0.75	x	$500 )
	=	$1,150,000	+	$1,125,000
	=	$2,275,000

Number of cases	=	Population	x	Disease Incidence rate
	=	280,000,000	x	0.075
	=	21,000,000

COI	=	Number of cases	x	( Average direct cost per case	+	Average indirect cost per case )
	=	21,000,000	x	( $86	+	$190 )
	=	$5,796,000,000

Present value calculator
Quantity	Value	Range
Discount rate (%)		0–10
Year number		1–100
Discount factor

Future value ($)		0–999999
Present value ($)

General price level increase	=	(166.6 – 163) / 163
	=	3.6 / 163
	=	0.022
	=	2.2%

Cost1999	=	Price1998	x	(CPI1999 / CPI1998)
	=	$23	x	(166.6 / 163)
	=	$23	x	1.022
	=	$23.50

=	$100,000	x	0.9709	+	$125,000	x	0.9426	+	$150,000	x	0.9151	+
	$200,000	x	0.8885	+	$125,000	x	0.8626

PV of scrap value	=	$5,000	x	1 / (1 + 0.05)¹⁰
	=	$5,000	x	0.6139
	=	$3069